# exponen dan logaritma

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## Presentation Transcript

### Slide 1:

ExpoNent, Roots, & Logarithm Exponent Formula CHAPTER I

### Slide 2:

Consider the following the problem What’s the product of 24 and 25? Solutions: am= a.a.a…..a m times 24= 2.2.2.2 =16 4 times 25=2.2.2.2.2 =32 So that the answer of the problem above is: 24.25 = 16.32 = 512 We know : 512 = 29 =16.32 =24.25 = 2 4+5 A. Exponent, Roots, And Logarithm

### Slide 3:

If we replace the base a by a, the exponents 4 and 5 by positive integers m and n : We will get: am = a.a.a….a m times an = a.a.a….a n times am.an = (a.a….a).(a.a….a) m times n times = a.a.a……..a (m+n) times FORMULA I with condition a € R, a ? 0 a is called the base number and m,n is called exponent

### Slide 4:

if m>n, them use formula I, we shall obtain: am-n .an = am-n+n am-n .an = am Formula II an

### Slide 5:

pay attention the following problem : (am)n = am.am…..am n times = am+m+m….m = am.n Conclusion Formula III

### Slide 6:

If besides a we also use the base of b, then the form (ab)m. Can be defined : (ab)m = ab.ab……ab m times = (a.a.a.a).(b.b.b.b) m times m times Formula IV

### Slide 7:

So that by the same way we will get Conclusion : b? 0 Formula V Because : is not defined

### Example : Simplify! :

Example : Simplify!

### Slide 13:

B.Integers Exponents In this section we shall see that formula I-V hold for integers exponents, either positive, negative and zero If we substitute m = n use formula II we shall obtain Formula VI a € R, a ? 0

### Slide 14:

If we subsituty m=0 use formula II we will get Formula VII a € R, a ? 0

### Slide 15:

SIMPLIFY!! Examples

### Slide 20:

By the Formula I we obtain am.an = am+n If we substituting n=m, then we will get am.am = a2m so that a2m = a 2m =1 m =1/2 form a2m =a ,can be changed (am) 2 = a am = va a1/2 = va In general can written C. Fractional Exponent

### Slide 21:

In the fractional exponents: If is changed ,then we will get : n,m is positive integers Formula VIII

### Slide 22:

By the formula VIII: ,then if ,we obtain Formula IX Furthermore the formula I - IX,also hold for fractional exponents

### Slide 23:

Example Simplify and write down in positive exponents!

### Slide 24:

Simplify and write down in the roots form !

3. Evaluate!

### Slide 26:

4. Find the length of diagonal of rectangle if it has dimension length is cm and width is cm!

### Slide 33:

EXPONENT EQUATION Example : 1. Find the solution set :

### Slide 35:

Example : 1. Find the solution set :

### Slide 38:

Example : 1. Determine the solution set :

: 2 V

V V

### Slide 42:

D. Rational Numbers and Irrational Number (1) Rational Number Rational Number are numbers which can be put in a/b form with a and b are integers numbers and b ? 0. Example: 3 coz 3 can be stated in etc 0.444…= 0.4 can be stated in 1.12 can be stated in Notes ! The lines above 12(no.3)shows that 12 is repeated unlimitedly Generally ! Rational number are repeated decimals

### Slide 43:

(2) Irrational Numbers Irrational number are number which can’t be stated in Generally : Irrational numbers are unrepeated decimal Example! =1.4142135…. = 5.1461524…. Log 2 = 0.3010…. e =2.71828182….. coz can’t be put in

### Slide 44:

1.Please check whether the following form are rational or irrational. Examples

### Slide 46:

E. Root Form Root number are the rational number which the result are irrational EXAMPLE :

### Slide 47:

1. Please check whether the following forms are root forms or not Note : Ln = Log number with base e Ln x = elog x Excercise

### Slide 53:

E. Algebra Operation Of Root Form REMEMBER !!

### Slide 54:

1. Evaluate the value of the following root forms ANSWER Examples

### Slide 57:

1. Find the value of the following problem !! 2. Find 2p+2q, 4pq and p2+q2 ANSWER Home Work !!!

### Slide 62:

G. Rationalizing The Denominator A fractional of root on its denominator such as : Can be simplified by rationalizing

Examples

### Slide 65:

Logarithm Formula Excercise Logarithm

### Slide 66:

Logarithm Formula

### Slide 67:

BACK Logarithm Formula

NEXT

NEXT

NEXT

### Slide 83:

5. Find the value of x that fulfill of the following equation! ANSWER

### Slide 86:

1. Find the value of x that fulfill of the following equation !! ANSWER Home Work !!!

V

V

### Slide 91:

thanks for your Attention...! cReated by: alFAth and NUgz el-Saverzs united